Start solving the equation. Find the equation that is equivalent. \[ \sqrt{3 x-5}-5=3 \]

Step 1 ：Isolate the square root term on one side of the equation: \( \sqrt{3x - 5} = 8 \)

Step 2 ：Square both sides of the equation to eliminate the square root: \( (\sqrt{3x - 5})^2 = 8^2 \)

Step 3 ：Simplify the squared equation: \( 3x - 5 = 64 \)

Step 4 ：Solve for x: \( 3x = 69 \)

Step 5 ：Divide both sides by 3: \( x = 23 \)

Step 6 ：Check the solution by plugging it back into the original equation: \( \sqrt{3(23) - 5} - 5 = 3 \)

Step 7 ：Simplify the check: \( \sqrt{64} - 5 = 3 \)

Step 8 ：Verify the solution: \( 8 - 5 = 3 \)

Step 9 ：Since the solution checks out, the final answer is \(\boxed{23}\)